Design of a nonlinear H/sub ∞/ state feedback controller for bilinear systems with nonlinear weight

Shimizu, Etsuro; Sampei, Mitsuji; Koga, Masanobu

doi:10.1109/cdc.1997.657125

Cited by 9 publications

(7 citation statements)

References 3 publications

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“…Recent work [13] performs nonlinear H ∞ control design of semi-active automotive suspensions. By restricting the nonlinear constrained weights on controlled signals, the Hamilton-Jacobi inequality is condensed into an algebraic Riccati inequality [14]. Although a smooth nonlinear control is guaranteed, this approach does not ensures the dissipative condition in design stage.…”

Section: Introductionmentioning

confidence: 99%

Sub-optimal control design of a semi-active vibration reduction system

Wang

Utsunomiya

2013

2013 American Control Conference

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This paper considers the vibration reduction of transportation systems using semi-active actuators to improve the ride quality. Control design for the resultant semi-active system is difficult for nonlinear dynamics, constrained control, lack of performance-oriented nonlinear control design, and limited state information. A sub-optimal control structure is proposed to address the performance requirement by mimicking the optimal control. A specific sub-optimal control is provided and implemented with one measurement to reduce the hardware cost. Performance analysis of the sub-optimal control is investigated. The semi-active system with the suboptimal control is simulated to demonstrate the effectiveness. American Control Conference (ACC)This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. Sub-optimal control design of a semi-active vibration reduction system Yebin Wang and Kenji UtsunomiyaAbstract-This paper considers the vibration reduction of transportation systems using semi-active actuators to improve the ride quality. Control design for the resultant semi-active system is difficult for nonlinear dynamics, constrained control, lack of performance-oriented nonlinear control design, and limited state information. A sub-optimal control structure is proposed to address the performance requirement by mimicking the optimal control. A specific sub-optimal control is provided and implemented with one measurement to reduce the hardware cost. Performance analysis of the sub-optimal control is investigated. The semi-active system with the suboptimal control is simulated to demonstrate the effectiveness.

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Section: Introductionmentioning

confidence: 99%

Sub-optimal control design of a semi-active vibration reduction system

Wang

Utsunomiya

2013

2013 American Control Conference

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“…x b (t) x r (t) − x w (t) Shimizu et al (1997) cannot be applied to this example with this weights. The objective of the robust control to be concerned is to minimize the effect of the disturbance (the road roughness) on the velocity of the car body, which is formulated as the problem of minimizing the following L 2 -induced norm:…”

Section: Numerical Examplementioning

confidence: 99%

“…To formulate the problem of finding such controllers Shimizu et al (1997) introduce nonlinear weights on z. It is shown by them that the obvious solution (the zero input) can be avoided by introducing the nonlinear weights.…”

Section: Plant and Nonlinear Weightsmentioning

confidence: 99%

“…It is shown by them that the obvious solution (the zero input) can be avoided by introducing the nonlinear weights. As in the paper of Shimizu et al (1997) we will also introduce nonlinear weights on z as shown in Fig. 3 where a z (x) and a u (x) are the nonlinear weights which are functions of x.…”

Section: Plant and Nonlinear Weightsmentioning

confidence: 99%

“…However, in the case of bilinear systems the usual L 2 -induced norm minimization problem leads to an obvious solution (the zero input is optimal!). To avoid the obvious solution Shimizu et al (1997) introduced nonlinear weights on the evaluated signal and proposed a design method using linearization of the state-dependent matrix Riccati inequality derived from the Hamilton-Jacobi equation. In contrast to this, the purpose of this paper is to propose a new design method using SOS (Sum-of-Squares) optimization without linearization.…”

Section: Introductionmentioning

confidence: 99%

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